• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.457-476
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• 2000

In this study, we have proposed a sampling method and an estimation method for efficiently estimating the mean of a population which has a linear trend. These methods involve drawing a sample by the so-called "centered balanced systematic sampling", which is an extension of systematic sampling, and then estimating the population mean with an adjusted estimator, not with the sample mean itself. We used the concept of interpolation in determining the adjusted estimator.\Ve compared the efficiency of the proposed estimator with those of the estimators from existing methods, under the expected mean square error criterion based on the infinite superpopulation model introduced by Cochran(1946). The proposed method is for use in the case when the sample size n(2 5) is an odd number and k(the reciprocal of the sampling fraction) is an even number. A good result was also obtained in an example using computer simulation. simulation.

• The Korean Journal of Applied Statistics
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• v.30 no.2
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• pp.301-309
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• 2017

It is often possible to test for differences in population means when two or more samples are extracted from each N population. However, it is not possible to test for the mean difference if one sample is extracted from each population since a sample mean does not exist. But, by dividing a group of samples extracted one by one into two groups and generating a sample mean, we can identify a heterogeneity that may exist within the group by comparing the differences of the groups' mean. Therefore, we propose a minimum combination t-test method that can test the mean difference by the number of combinations that can be divided into two groups. In this paper, we proposed a method to test differences between means to check heterogeneity in a group of extracted samples. We verified the performance of the method by simulation study and obtained the results through real data analysis.

• Communications for Statistical Applications and Methods
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• v.26 no.6
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• pp.611-622
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• 2019

This paper considers the estimation of the long memory parameter in nonparametric regression with strongly correlated errors. The key idea is to minimize a unified mean squared error of long memory parameter to select both kernel bandwidth and the number of frequencies used in exact local Whittle estimation. A unified mean squared error framework is more natural because it provides both goodness of fit and measure of strong dependence. The block bootstrap is applied to evaluate the mean squared error. Finite sample performance using Monte Carlo simulations shows the closest performance to the oracle. The proposed method outperforms existing methods especially when dependency and sample size increase. The proposed method is also illustreated to the volatility of exchange rate between Korean Won for US dollar.

• Journal of Korean Society for Quality Management
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• v.22 no.1
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• pp.152-161
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• 1994

In this paper we develop a test for alternatives representing decreasing mean residual life. The test statistic for decreasing mean residual life, $K_{1n}$, is a modified version of Hollander and Proschan's test $V^*$ and critical constants and large sample approximation are shown to make the test readily applicable. Consistency is also shown for the tests based on $K_{1n}$. And small sample powers for four alernatives are obtained.

• Journal of Integrative Natural Science
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• v.10 no.1
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• pp.33-39
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• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-q{\geq}3)$, $q=rank(P_V)$ with a projection matrix $P_v$ under the quadratic loss, based on a sample $X_1$, $X_2$, ${\cdots}$, $X_n$. We find a James-Stein type decision rule which shrinks towards projection vector when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-P_V{\theta}{\parallel}$ is restricted to a known interval, where $P_V$ is an idempotent and projection matrix and rank $(P_V)=q$. In this case, we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.443-449
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• 2017

Estimation of population proportion like the distribution rate of LED TV and the prevalence of a disease are often estimated based on survey sample data. Population proportion is generally considered as a special form of population mean. In complex sampling like stratified multistage sampling with unequal probability sampling, the denominator of mean may be random variable and it is estimated like ratio estimator. In this research, we examined the estimation of distribution rate based on stratified multistage sampling, and determined some numerical outcomes using stratified random sample data with about 25% of missing observations. In the data used for this research, the survey weight was determined by deterministic way. So, the weights are not random variable, and the population distribution rate and its variance estimator can be estimated like population mean estimation. When the weights are not random variable, if one estimates the variance of proportion estimator using ratio method, then the variances may be inflated. Therefore, in estimating variance for population proportion, we need to examine the structure of data and survey design before making any decision for estimation methods.

• Journal of Integrative Natural Science
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• v.12 no.3
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• pp.91-99
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• 2019

Many researchers in various study fields use the two sample t-test to confirm their treatment effects. The two sample t-test is generally used for small samples, and assumes that two independent random samples are selected from normal populations, and the population variances are unknown. Researchers often conduct F-test, the test of equality of variances, before testing the treatment effects, and the test statistic or confidence interval for the two sample t-test has two formats according to whether the variances are equal or not. Researchers using the two sample t-test often want to know how large sample sizes they need to get reliable test results. This research gives some guidelines for sample sizes to them through simulation works. The simulation had run for normal populations with the different ratios of two variances for different sample sizes (${\leq}30$). The simulation results are as follows. First, if one has no idea equality of variances but he/she can assume the difference is moderate, it is safe to use sample size at least 20 in terms of the nominal level of significance. Second, the power of F-test for the equality of variances is very low when the sample sizes are small (<30) even though the ratio of two variances is equal to 2. Third, the sample sizes at least 10 for the two sample t-test are recommendable in terms of the nominal level of significance and the error limit.

• Journal of the Korean Data and Information Science Society
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• v.13 no.1
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• pp.147-156
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• 2002

In this paper, we study the properties of the modified winsorized mean to estimate the mean of a two-truncation parameter population. Under some mild conditions, the estimator is found to be strongly consistent and asymptotically unbiased even though the sample is doubly type II censored.

• Journal of Korean Society for Quality Management
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• v.26 no.4
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• pp.101-110
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• 1998

The mean residual life function is the expected remaining life of an item at age $\chi$. The problem of trend change in the mean residual life is great interest in the reliability and survival analysis. In this paper we develop a new test statistic for testing whether or not the mean residual life changes its trend based on a complete sample. Monte Carlo simulations are conducted to compare the perfor mance of our test statistic with that of previously known tests.

• Journal of the korean society of oceanography
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• v.33 no.3
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• pp.113-122
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• 1998

The requisite numbers of sample replicates for the population study of soft-bottom benthos were estimated from survey data on the Songdo tidal flat and subtidal zone in Youngil Bay, Korea. Large numbers of samples were taken; two-hundred-fifty 0.02 m$^2$ box corers and fifty 0.1m$^2$ van Veen grabs were taken on the Songdo tidal flat and in Youngil Bay, respectively. The effect of sampler size on sampling efforts was investigated by pooling the unit samples in pairs, fours, eights, etc. The requisite number of sample replicates (n$_r$) was determined by sample variance (s$^2$) and mean (m) function (n$_r$:s$^2$/P$^2$m$^2$), at P=0.2 level, in which s$^2$ and m were calculated from the counts of individuals collected. For example, seven samples of 0.02 m$^2$ corer for the intertidal and two samples of 0.1 m$^2$ van Veen grab for subtidal fauna were required to estimate the total density of community. The smaller sampler size was more efficient than larger ones when sampling costs were compared on the basis of the total sampling area. The requisite number of sample replicates was also predicted ($\^{n}$n$_r$) by substituting $\^{s}$$^2$ obtained from the regression of s$^2$ against m using the Taylor's power law ($\^{s}$$^2$:am$^b$). The regression line of survey data on s$^2$ and m plotted on log scale was well fitted to the Taylor's power law (r$^2$${\geq}$0.95, p<;0.001) over the whole range of m. The exponent b was, however, varied when it was estimated from m which was categorized into classes by its scale. The fitted exponent b was large when both density class and the sampler size were large. The number of sample replicates, therefore, could be more significantly estimated, if regression coefficients (a and b) would be calculated from sample variance and mean categorized into density classes.